The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8
Given are the list of the rational numbers, so,
1 4/5, -7/4, 41% and -1.3
So,
1) The fraction form :-
a) 1 4/5 = 9/5
b) -7/4
c) 41% = 41/100
d) -1.3 = 13/10
2) The decimal form :-
a) 1 4/5 = 9/5 = 1.8
b) -7/4 = -1.75
c) 41% = 41/100 = 0.41
d) -1.3 = 13/10 = -1.3
3) The ascending order of the rational numbers =
You can arrange them by seeing the value and sign,
-1.75 < -1.3 < 0.41 < 1.8
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An apartment building has 9 apartments that are being rented. The data shows the monthly rent for each apartment.
$1,710 $1,515 $1,410 $1,435 $1,555 $1,595 $1,690 $1,575 $1,640
Create a stem display for this data.
The stem display for the data, given the monthly rent and the apartment building is:
$14 | 10 15 35
$15 | 15 55 75 95
$16 | 40 90
How to make the stem display ?To create a stem display, we first divide the data into groups of tens. The first group is $ 1400 -$ 1499, the second group is $ 1500 - $1599 , and so on. Next, we write the units digit of each number in the appropriate group.
For example, the number 1,710 is in the $ 1500 - $ 1599 group, so we write a 1 in the 15 column. Finally, we count the number of numbers in each group. There are three numbers in the $ 1400 - $ 1499 group, two numbers in the $ 1500 - $ 1599 group, and three numbers in the $ 1600 - $ 1699 group.
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Find the value of c guaranteed by the Mean Value Theorem……
As per the given equation, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).
To find the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3], we need to determine if the conditions of the Mean Value Theorem are satisfied and then find the value of c.
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).
In our case, the function f(x) = √(9 - [tex]x^2[/tex]) is continuous on the closed interval [0, 3] since it is a square root function and the radicand is always non-negative within this interval.
The function is also differentiable on the open interval (0, 3) since it is the square root of a differentiable function.
To find the value of c, we first calculate f(3) and f(0):
f(3) = √(9 - [tex]3^2[/tex]) = √(9 - 9) = √0 = 0
f(0) = √(9 - [tex]0^2[/tex]) = √(9 - 0) = √9 = 3
Next, we calculate f'(c):
f'(x) = (-2x)/√(9 - x^2)
We want to find the value of c such that f'(c) = (f(3) - f(0))/(3 - 0). Let's substitute the values into the equation:
(-2c)/√(9 - [tex]c^2[/tex]) = (0 - 3)/(3 - 0)
(-2c)/√(9 - [tex]c^2[/tex]) = -1
To solve for c, we can cross-multiply:
-2c = -√(9 - [tex]c^2[/tex])
Squaring both sides:
4c^2 = 9 - [tex]c^2[/tex]
Simplifying:
5[tex]c^2[/tex] = 9
Dividing both sides by 5:
[tex]c^2[/tex] = 9/5
Taking the square root of both sides:
c = ± √(9/5)
Therefore, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).
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A rental company charges $75 a day and 25 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill came to $243. How many miles did he drive?
The calculated total distance he drive is 372 miles
How many miles did he drive?From the question, we have the following parameters that can be used in our computation:
Charges $75 a day25 cents a mileSo, we have
Total charges = 75 * days + 0.25 * miles
For 2 days and total ot 243. we have
75 * 2 + 0.25 * miles = 243
So, we have
miles = 372
Hence, the total distance he drive is 372 miles
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Find the area of this triangle
The calculated area of the triangle is 38.30 square units
How to find the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
The area of the triangle is calculated as
Area = 1/2absin(c)
Where
a = b = 10
c = 50 degrees
Using the above as a guide, we have the following:
Area = 1/2 * 10 * 10 * sin(50 degrees)
Evaluate
Area = 38.30
Hence, the area of the triangle is 38.30 square units
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please help! thank uu ~ :) please be correct!
Answer:
look at explanation
Step-by-step explanation:
50/50 chance
A circle has a center at C(2,7). The point A(8,17) lies on the circle. Which of the
following is the slope of the tangent to the circle at point A?
The slope of the tangent to the circle at point A is -3/2.
1. The equation of a circle with center C(2, 7) is given by (x - 2)² + (y - 7)² = r², where r is the radius of the circle.
2. Since point A(8, 17) lies on the circle, we can substitute the coordinates of point A into the equation of the circle to find the value of r.
(8 - 2)² + (17 - 7)² = r²
6² + 10² = r²
36 + 100 = r²
136 = r²
r = √136 = 2√34
3. Now that we have the radius, we can find the equation of the tangent line at point A.
The tangent to a circle at a given point is perpendicular to the radius at that point.
The slope of the radius can be found using the coordinates of the center and point A.
Slope of the radius = (17 - 7) / (8 - 2) = 10 / 6 = 5/3
The slope of the tangent line will be the negative reciprocal of the slope of the radius.
Slope of the tangent = -1 / (5/3) = -3/5
4. However, the question asks for the slope of the tangent to the circle at point A, so we need to consider the slope of the tangent line at point A, which is the negative inverse of the slope of the radius.
Slope of the tangent at point A = -1 / (5/3) = -3/5
5. The slope of the tangent to the circle at point A is -3/5.
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Find the measure of the red arc or chord in ⊙C
The calculated measure of the red arc in ⊙C is 5
How to find the measure of the red arc or chord in ⊙C.From the question, we have the following parameters that can be used in our computation:
The circle
From the circle, we have
Centers = C
Also, we have
Corresponding segments are equal segments
Using the above as a guide, we have the following:
UV = TU
Where
TU = 5
This gives
UV = 5
Hence, the value of UV is 5
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5 years ago the ratio of mark's age was 3:4 mark is 12 yr younger than francis how old is francis now.
5 years ago the ratio of Mark's age was 3:4 mark is 12 yr younger than Francis, now Francis is currently 53 years old
Let us suppose that age of him 5 years ago was 3x and Francis's age 5 years ago was 4x. According to the given information, Mark is 12 years younger than Francis.
So, we can set up the equation: 3x + 12 = 4x.
Simplifying the equation, we have: 12 = x.
This means that 5 years ago,
Mark age = 3 * 12 = 36 years old,
Francis age = 4 * 12 = 48 years old.
Now, to find out how old Francis is now, we add 5 years to both Mark and Francis. Thus, Francis's current age is 48 + 5 = 53 years.
Therefore, Francis is currently 53 years old.
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Suppose that on January 1 you have a balance of $3100 on a credit card whose APR is 17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1
.a. Calculate your monthly payments.
b. When the card is paid off, how much will you have paid since January 1?
c. What percentage of your total payment from part (b) is interest?
a. Your monthly payments would be approximately $275.49.
b. When the card is paid off, you will have paid approximately $3,305.88 since January 1.
c. The percentage of your total payment that is interest is approximately 6.3%.
To calculate the monthly payments, we first need to determine the interest rate per month.
Since the APR is 17%, we divide it by 12 to get the monthly interest rate: 17% / 12 = 1.42%.
a. Monthly payments:
To pay off the credit card balance in one year (12 months), we divide the total balance by the number of months:
$3100 / 12 = $258.33 (approximately)
Therefore, your monthly payment should be approximately $258.33.
b. Total amount paid:
To calculate the total amount paid since January 1, we multiply the monthly payment by the number of months (12):
$258.33 * 12 = $3,099.96
Therefore, you will have paid approximately $3,099.96 since January 1.
c. Percentage of payment as interest:
To determine the percentage of the total payment that is interest, we subtract the initial balance from the total amount paid to find the total interest paid:
Total interest = Total amount paid - Initial balance
Total interest = $3,099.96 - $3100
Total interest = $-0.04 (approximately)
The negative value implies that the balance was paid off completely before the end of the year, resulting in a small overpayment.
As a result, there is no interest to calculate as it has been paid in full.
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A rock is thrown from the top of a building. The height s (in feet) as a function of time (in seconds) can be modeled by the function
s(t) = -16t² + 3000
Approximately when will the rock be 1,976 feet above the ground.
O a
Ob
C
8 sec
135 sec
85 sec
15 sec
Answer: the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds
Step-by-step explanation:
We can start by setting the height function equal to 1,976 and solving for t:
-16t² + 3000 = 1976
Subtracting 1976 from both sides, we get:
-16t² + 1024 = 0
Dividing both sides by -16, we get:
t² - 64 = 0
Factoring, we get:
(t + 8)(t - 8) = 0
So t = 8 or t = -8. We can ignore the negative solution since time cannot be negative.
Therefore, the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds.
Answer: (A) 8 sec
Determine the lengths of the missing sides x and y in the triangle below:
x =
y =
2.6 2.1 4.2 3
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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Can I have help, please?
You are willing to pay $5 a pound for dog food. Your local pet store sells dog food at $4 a pound. What is the consumer surplus?
The consumer surplus for the price of the dog food is given as follows:
$1.
How to calculate the consumer surplus?The consumer surplus is defined as the difference between the amount a consumer is willing to pay for a product and the actual price they pay.
The parameters in the context of this problem are given as follows:
The consumer is willing to pay $5 for the pound of dog food.The local pet store sells the pound of dog food for $4.Hence the consumer surplus for the price of the dog food is given as follows:
5 - 4 = $1.
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An airplane is cruising at a rate of 550 miles per hour. Write an equation that shows the relationship between the number of hours of cruising, x, and the number of miles traveled, y.
Answer: y = 550x
Step-by-step explanation:
Two coins are tossed. What is the probability of both coins landing on heads?
1/4 or 0.25 is the probability of both coins landing on heads.
When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), or one coin can land on heads while the other lands on tails (HT or TH).
To find the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) and divide it by the total number of possible outcomes. The number of favorable outcomes is 1 (HH), as there is only one way for both coins to land on heads.
The total number of possible outcomes is 2 * 2 = 4, since each coin has two possible outcomes (heads or tails), and we multiply them together to account for all possible combinations.
Therefore, the probability of both coins landing on heads is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 4
Simplifying the fraction, we get:
Probability = 1/4
So, the probability of both coins landing on heads is 1/4 or 0.25.
This means that out of all the possible outcomes when two coins are tossed, there is a 1 in 4 chance that both coins will land on heads. It's important to note that the probability assumes fair and unbiased coins, where the chance of heads and tails is equal.
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a function is in the form g(x)= ax2 + d. if a is greater than 1 and d is positive, which could be the graph of g(x) ?
hello
to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file
(a) In the figure below, m AB = 106° and m CD =66. Find mAEB
Answer:
[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]
Step-by-step explanation:
Given:arc AB = 106°
arc CD = 66°
Statement:According to angles of intersecting chords theorem, the measure of angle formed by two intersecting chords is half the sum of arcs intercepted by the angle.Mathematical form:[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]
Solution:Put the given data in the above formula.
[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]
Answer all of these pls
1. -3x+7=-8x+47
2. -13x+8=-8x-7
3. 6x+7=3x+19
4. 12x-8=10x+6
5. -7x-4=-10x-10
6. 7x-9=3x-5
7. 3x-9=5x-3
8. 7x-1=5x+5
9. -7x-2=-3x-14
10. -3x-7=-8x-57
Answer:
Sure, I'd be happy to help you solve these equations! Here are the solutions to the equations you provided:
1. -3x+7=-8x+47
Add 8x to both sides: 5x + 7 = 47
Subtract 7 from both sides: 5x = 40
Divide both sides by 5: x = 8
2. -13x+8=-8x-7
Add 13x to both sides: 5x + 8 = -7
Subtract 8 from both sides: 5x = -15
Divide both sides by 5: x = -3
3. 6x+7=3x+19
Subtract 3x from both sides: 3x + 7 = 19
Subtract 7 from both sides: 3x = 12
Divide both sides by 3: x = 4
4. 12x-8=10x+6
Subtract 10x from both sides: 2x - 8 = 6
Add 8 to both sides: 2x = 14
Divide both sides by 2: x = 7
5. -7x-4=-10x-10
Add 10x to both sides: 3x - 4 = -10
Add 4 to both sides: 3x = -6
Divide both sides by 3: x = -2
6. 7x-9=3x-5
Subtract 3x from both sides: 4x - 9 = -5
Add 9 to both sides: 4x = 4
Divide both sides by 4: x = 1
7. 3x-9=5x-3
Subtract 3x from both sides: -6 = 2x - 3
Add 3 to both sides: -3 = 2x
Divide both sides by 2: x = -3/2 or -1.5
8. 7x-1=5x+5
Subtract 5x from both sides: 2x - 1 = 5
Add 1 to both sides: 2x = 6
Divide both sides by 2: x = 3
9. -7x-2=-3x-14
Add 3x to both sides: -4x - 2 = -14
Add 2 to both sides: -4x = -12
Divide both sides by -4: x = 3
10. -3x-7=-8x-57
Add 8x to both sides: 5x - 7 = -57
Add 7 to both sides: 5x = -50
Divide both sides by 5: x = -10
I hope this helps! Let me know if you have any further questions.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The percentage of vehicles that are returned with less than 30000 miles are given as follows:
b) 2.5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 36400, \sigma = 3200[/tex]
The proportion is the p-value of Z when X = 30000, hence:
Z = (30000 - 36400)/3200
Z = -2.
Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.
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Calculate the bearing of Y from X
Answer:
074°
Step-by-step explanation:
the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY
∠ NXY = 180° - 106° = 74°
the 3- figure bearing of Y from X is 074°
What are the x-intercepts of the quadratic function? (1 point)
parabola going down from the left and passing through the point negative 3 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 6 and 2 comma 0
(0, −3) and (0, 2)
(0, −6) and (0, 6)
(−3, 0) and (2, 0)
(−6, 0) and (6, 0)
Answer:
The x-intercepts are (-3, 0) and (2, 0).
Math
82°F
Algebra 1 CC.20 Checkpoint: Quadratic equations NXG
2
x² - y + x = 16
y = 3x + 2
3x² - y + 32 = 22x
y = 2x - 16
Language arts
Decide whether each system of equations has two real solutions, exactly one real solution, or
no real solutions.
y = -x² + 6x + 12
y = -x +3
Answer:
x² - y + x = 16 is 1 real solution
3x² - y + 32 = 22x is 2 real solutions
y = -x² + 6x + 12 is 1 real solution
Step-by-step explanation:
sorry i am unsure about rest, they do not have a value. good luck :)
Choose the function whose graph is given by:
AMMA
+²
OA. y = cos(4x)
OB. y = cos(x)
OC. y = cos(2x)
OD. y = cos(x)
The graph of the function y=cos(x) is shown below:
[Image of the graph of the function y=cos(x)]
The graph of the function y=cos(2x) is shown below:
[Image of the graph of the function y=cos(2x)]
The graph of the function y=cos(4x) is shown below:
[Image of the graph of the function y=cos(4x)]
As you can see, the graph of the function y=cos(4x) is the same as the graph of the function y=cos(x), but it is compressed horizontally by a factor of 4. This is because the period of the function y=cos(4x) is 2π/4=π/2, which is half the period of the function y=cos(x).
Therefore, the correct answer is A.
You have a bag of 12 blue marbles (numbered 1-12) and 12 red marbles (numbered 1-12). So you have 24 marbles in total (half blue and half red) with each of the numbers 1-12 appearing twice (once in each color). You draw one marble at random, replace it to the bag, mix up the marbles, and draw a second marble. Determine each of the following probabilities. P ( first marble is blue and second marble is red ) =
The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.
To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag
In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.
When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.
After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.
To find the overall probability, we multiply the probabilities of each event since they are independent events:
P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)
[tex]= (12/24) \times (12/24)[/tex]
[tex]= (1/2) \times (1/2)[/tex]
= 1/4.
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Brian says the graph shows the circle with a center (-3, 2) and a radius of 3. Mia says the graph shows all possible centers for a circle that passes through (3, -1) with a radius of 4. Which student is correct? Explain.
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
The graph represents a specific circle with its own center and radius.
To find all possible centers for a circle passing through a given point, we need to consider the locus of points equidistant from the given point.
In this case, the locus of points equidistant from (3, -1) with a radius of 4 forms another circle with a different center and radius.
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
Therefore, neither student's claim is correct based on the given information.
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What is the slope of the line that passes through the points (2,-4) and (5, 2)? Write
your answer in simplest form.
Answer:
undefined
Submit Answer
attempt 1 out of 2
Answer:
1/2
Step-by-step explanation:
Slope formula:
[tex] \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}[/tex]
P.S. Slope is denoted by letter m
We have;
[tex]x_{1}, y_{1}[/tex] = (2,-4)[tex]x_{2}, y_{2}[/tex] = (5,2)[tex] \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }[/tex]
[tex] \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }[/tex]
[tex] \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} [/tex]
please help its due today and I need a good grade on it!!!!
The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².
To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,
We can use the standard equation for a parabola in vertex form:
y = a(x - h)² + k
In this equation, (h, k) represents the coordinates of the vertex.
Since we want the vertex to be at the origin (0, 0), the equation becomes:
y = ax²
To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.
Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.
In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).
Plugging in the value of f (8) into the formula, we can solve for 'a':
8 = 1/(4a)
32a = 1
a = 1/32
Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²
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The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?
x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
A f(x), because it eventually exceeds g(x)
B g(x), because it eventually exceeds f(x)
C f(x), because it eventually intersects g(x)
D g(x), because it will not intersect f(x)
The function g(x) is increasing exponentially because it eventually exceeds f(x).
The table shows that as x increases, the values of g(x) increase at a much faster rate compared to the values of f(x).
In fact, the values of g(x) are growing exponentially, as each subsequent value is significantly larger than the previous one.
Therefore, the function g(x) is most likely increasing exponentially.
Thus, g(x) is increasing exponentially because it eventually exceeds f(x).
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The following table gives the number of women age 16 years and older (in
millions) in a country's civilian workforce for selected years from 1950 and
projected to 2050.
Complete parts (a) and (b) below.
CTTS
X+
Women in the
Year Workforce (millions)
1950
1960
1970
1980
1990
2000
18.2
21.3
31.7
45.5
554
65.5
a. Use x as the number of years past January 1st, 1950 to create a cubic model, y, using these data.
y=x²+x+x+
4
(Type integers or decimals rounded to five decimal places.)
Clear all
Women in the
Year Workforce (millions)
2010
2015
2020
2030
2040
2050
75.3
78.1
78.5
80.5
86.6
91.5
Check answer
The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
How to calculate the valueLet's set up a system of equations using the given data points:
For x = 0 (year 1950):
18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2
For x = 10 (year 2000):
65.5 = a(10)³ + b(10)² + c(10) + 18.2
For x = 20 (year 2010):
75.3 = a(20)³ + b(20)² + c(20) + 18.2
For x = 25 (year 2015):
78.1 = a(25)³ + b(25)² + c(25) + 18.2
For x = 30 (year 2020):
78.5 = a(30)³ + b(30)² + c(30) + 18.2
For x = 40 (year 2030):
80.5 = a(40)³ + b(40)² + c(40) + 18.2
For x = 50 (year 2040):
86.6 = a(50)³ + b(50)² + c(50) + 18.2
For x = 60 (year 2050):
91.5 = a(60)³ + b(60)² + c(60) + 18.2
Simplifying these equations, we have: d = 18.2
1000a + 100b + 10c + 18.2 = 65.5
8000a + 400b + 20c + 18.2 = 75.3
15625a + 625b + 25c + 18.2 = 78.1
27000a + 900b + 30c + 18.2 = 78.5
64000a + 1600b + 40c + 18.2 = 80.5
125000a + 2500b + 50c + 18.2 = 86.6
216000a + 3600b + 60c + 18.2 = 91.5
We can solve this system of equations to find the coefficients a, b, and c.
Using a cubic regression calculator or a matrix solver, the solution is:
a ≈ 0.00006204
b ≈ 0.00231059
c ≈ -0.10811757
Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
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23. Solve for the missing variables.
The values of the missing variables are:
a = 57
b = 75
c = 96
d = 150
We have,
Angle 48 is half the intercepted arc.
So,
1/2 x c = 48
c = 48 x 2
c = 96
Now,
Similarly
Angle a = 1/2 x 114
Angle a = 57
And,
The sum of the angles in a triangle = 180
a + b + 48 = 180
57 + b + 48 = 180
b = 180 - (57 + 48)
b = 180 - 105
b = 75
Now,
Angle b = 1/2 x d
75 = 1/2 x d
d = 75 x 2
d = 150
We can also see that,
114 + c + d = 360
114 + 96 + 150 = 360
360 = 360
Thus,
The values of the missing variables are:
a = 57
b = 75
c = 96
d = 150
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